Apparatus with resolution enhancement feature for improving accuracy of conversion of required chemical mechanical polishing pressure to force to be applied by polishing head to wafer

ABSTRACT

CMP systems move a polishing pad relative to a wafer and a retainer ring and implement instructions to apply required pressure to the wafer for CMP operations. Accuracy of computations of the pressures, and of conversion of the pressure to force, is improved without use of high resolution components, such as high resolution digital devices, using both digital and analog operations, and by converting values of required pressure or force from one set of units to a second set of units and then back to the first set of units. A quantization process is performed using data processed by average resolution digital devices. The process transfers both pressure/force scale and pressure/force set point data between separate processors to obtain computed values of pressure and force having acceptable accuracy, eliminating quantization errors are eliminated or significantly reduced.

RELATED APPLICATIONS

[0001] The present application is a divisional of co-pending U.S. patentapplication Ser. No. 09/823,151, filed on Mar. 29, 2001, entitled“APPARATUS AND METHODS WITH RESOLUTION ENHANCEMENT FEATURE FOR IMPROVINGACCURACY OF CONVERSION OF REQUIRED CHEMICAL MECHANICAL POLISHINGPRESSURE TO FORCE TO BE APPLIED BY POLISHING HEAD TO WAFER”, by MiguelA. Saldana (the “Parent Application”), priority under 35 U.S.C. 120 ishereby claimed based on the Parent Application, and such ParentApplication is hereby incorporated by reference.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates generally to high performancesystems and techniques for polishing workpieces. Specifically, thepresent invention relates to chemical mechanical polishing (CMP)apparatus for improving the accuracy of conversion of data representingrequired CMP pressures to data representing CMP forces to be applied bya polishing (or planarization) head to a workpiece such as asemiconductor wafer, wherein quantization errors are minimized eventhough components having average resolution are used to provide some ofthe data used in the conversion operations.

[0004] 2. Description of the Related Art

[0005] In the fabrication of semiconductor devices, CMP operations areperformed for buffing, cleaning, planarization, and polishing of wafers.A typical semiconductor wafer may be made from silicon and may be a diskthat is 200 mm or 300 mm in diameter. The term “wafer” is used below todescribe and include such semiconductor wafers and other planarstructures, or substrates, that are used to support electrical orelectronic circuits.

[0006] As integrated circuit device complexity increases, there is anincreased need to improve the accuracy of CMP operations for planarizingdielectric materials deposited onto wafers. Also, as more metallizationline patterns are formed in the dielectric materials, there is anincreased need for higher accuracy in CMP operations that remove excessmetallization.

[0007] In a typical CMP system, a wafer is mounted on a carrier with asurface of the wafer exposed. The carrier and the wafer rotate in adirection of rotation. The CMP process may be achieved, for example,when the exposed surfaces of the rotating wafer and of a polishing padare urged into contact with each other by a polishing force, and whenthe wafer and the polishing pad move laterally relative to each other.

[0008] Two aspects of achieving accuracy of the polishing force appliedto a wafer are of interest. Once a value of a required polishingpressure is specified, that value must first be accurately converted toa corresponding required force and then to a required force signal thataccurately represents the required force. The force signal is applied toa force-producing device. Secondly, the actual force applied by theforce-producing device must be measured and fed back to adjust the forcesignal. Improvements have been made to facilitate making repeatablemeasurements of the actual polishing forces applied to the wafer.However, there is still a need to more accurately convert the value ofthe required pressure to the value of the force signal. Such needexists, for example, in CMP systems in which the value of the requiredCMP force must be rapidly changed in relation to rapidly changing valuesof the exposed area of the wafer that is in contact with the polishingpad as the lateral position of the polishing pad changes relative to thewafer. CMP systems and methods in which the value of the requiredpolishing forces are rapidly changed according to such rapidly changingvalues of the contact areas are described in co-pending U.S. patentapplication Ser. No. 09/748708, filed Dec. 22, 2000, entitled “POLISHINGAPPARATUS AND METHODS HAVING HIGH PROCESSING WORKLOAD FOR CONTROLLINGPOLISHING PRESSURE APPLIED BY POLISHING HEAD,” by Miguel A. Saldana andDamon V. Williams (the Prior Application). Such Prior Application ishereby incorporated by reference.

[0009] The CMP systems and methods of the Prior Application implement arecipe (or set of instructions) for laterally moving the polishing padrelative to a wafer carrier and to a retaining ring on the carrier. Therelative movement results in the rapidly changing values of the contactarea between the polishing pad and the exposed surface of the wafer, andbetween the pad and a conditioning puck. Feedback of polishing padposition is coordinated with determinations of required values of thevariable force by which such different contact areas are separatelyurged into contact with the polishing pad so that the pressure on eachsuch different contact area may be controlled. The feedback is generatedby an encoder that indicates the actual successive lateral positions ofthe polishing pad relative to the wafer, for example. The differentvalue of each such separate contact area is determined based on theoutput of the encoder. For each respective pair of one such contact areaand one such pressure to be applied to that contact area, a force signalis output (commanded) to represent a corresponding requested force. Eachrespective force signal is applied to the force-producing device (e.g.,an actuator) which provides the force by which the one such contact areaof the wafer, for example, is separately urged into contact with thepolishing pad at the particular time at which the actual lateralposition is measured.

[0010] Even though the invention of the Prior Application enablesconversions of the value of the required pressure to the force signal,there is a need to increase the resolution of the commanded force signalwhen the actuator that is used displays analog controllability betterthan that of conventional digital control methods. For example,conventional pneumatic actuators have a low (or coarse) resolution,which provides steps or increments of 2.5 pounds of force. With suchcoarse resolution, the actuator may be used with the conventionaldigital control methods having a 10 bit resolution, for example. Indetail, a range of polishing pressure may be 10 psi for a 200 mm waferthat has an area of about 50.26 square inches. The maximum force is502.6 pounds (10 psi×50.26 sq. in.). Force increments corresponding tothe 10 bits are about 0.49 pounds (the force divided by the 1024 stepsof the resolution). Thus, the increments of the mechanical resolutionare more coarse than the 10 bit digital increments. However, when theactuator is a high resolution actuator capable of applying force inincrements substantially less than 2.5 pounds (e.g., much less than theabove exemplary 0.49 pounds), the conventional digital control methodsdo not provide the small increments of the commanded force signal thatare necessary to take advantage of the high actuator resolution.

[0011] Another example illustrates errors that may result from use ofdevices having too low a resolution. Resolution is generally defined as2 bit, 4 bit, n bit, etc. The number of output signals (or counts orsteps) is 2 to the nth power. Thus, the very low 2 bit resolutioncorresponds to four counts or steps. In the context of theabove-described required pressure, the resolution of the above-describeddigital methods dictates aspects of the force computation for convertingthe required pressure to the required force and to the value of therequired force signal, and those aspects have an effect on accuracy. Forexample, the very low 2 bit resolution would correspond to a very low 2bit computational resolution. Use of the 2 bit computational resolutionwould provide that a 10 psi pressure range be divided into four parts,such as discrete steps at 2.5 psi intervals, i.e., pressure values of 0,2.5, 5.0, 7.5, and 10 psi. If the CMP system performs the conversioncomputations with respect to a required pressure having a value of 8.25psi, for example, the increments (or steps) of the pressure may be 0.25psi, which may be referred to as a parameter resolution increment. Also,7.5 psi would be the value of the available output pressure step that isclosest to the required 8.25 psi pressure. An accuracy problem resultingfrom such low resolution is shown by an example in which the requiredpressure value of 8.25 psi is to be input for processing. The conversioncomputation must convert the value of the required pressure (e.g., frompsi to counts to voltage to counts and back to psi). Ideally, after theconversions, the required pressure would be output as exactly 8.25 psi.However, if the very low 2 bit resolution is used, the value of therequired pressure would not exactly match the absolute value of any ofthe 0, 2.5, 5.0, 7.5, or 10 psi values of the steps of the pressurerange. Use of the 7.5 psi value to represent the required 8.25 psipressure would result in an error of 0.75 psi, or an error of 9.1percent (9.1%) of the required 8.25 psi. Such a large error in currentCMP systems would be unacceptable.

[0012] With this example in mind, the term “quantization” is used hereinto refer to a process of computation in which computational resolutionis of significant importance in obtaining a computed result having anacceptable accuracy. A “quantization process” is quantization in whichan initial value of a parameter is subjected to computational operationsto obtain the computed result. Such exemplary 9.1% error resulting fromthe above exemplary quantization is referred to herein as a“quantization error”. Generally, a high value of resolution results insteps having a small absolute value. With this in mind, in a normalsituation, an unacceptable quantization error may result from performingthe computation using too low a value of the computational resolution.For example, the above very low resolution may be the very lowcomputational resolution (2 bits). A high absolute value (2.5 psi) ofthe steps of the computational resolution in such example was determinedby dividing the count value of the very low 2 bit computationalresolution (i.e., 4) into the 10 psi pressure range. Such high absolutevalue of the computational steps results in fewer steps. On the otherhand, in the example the absolute value of the pressure (or parameter)increments (0.25 psi) is much less than the absolute value 2.5 psi. Asnoted above, the values of the exemplary 9.1% quantization error isunacceptable.

[0013] If a higher computational resolution were used, such as a 3 bitresolution, then the 10 psi pressure range would be divided by 8 (2 tothe third power), and each step based on the higher resolution wouldhave a smaller absolute value (1.25 psi). Use of the 1.25 psi absolutevalue steps would provide a computational step of 8.0 psi closest to theexemplary required 8.25 psi, and a quantization error of 0.25 psi, or3.03 percent (3.03%) of the required 8.25 psi. This example shows thatas the computational resolution increases, the number of stepsincreases, the value of each step decreases, and the quantization errordecreases.

[0014] The method of determining the quantization error in each of theabove-described examples is referred to as the “normal criteria” fordetermining whether an acceptable quantization error will result fromthe use of relatively low component resolution digital devices, such asdigital to analog converters and analog to digital converters. Suchnormal criteria is not based on the principles of the present invention.

[0015] Continuing to use such digital devices as one example of acomponent having an availability that decreases as resolution increases,such digital devices are essential in determining the values of thecommand signals (voltages) applied to the actuators. However, there islimited availability of such digital devices having high componentresolution (e.g., in excess of about 10 or 12 bits ). Reference is madeto the above-described need to increase the resolution of the commandedforce signal when the actuator that is used displays analogcontrollability better than that of conventional digital controlmethods. Such need to increase component resolution is in conflict withthe limited availability noted above. Therefore, as a basis for assuringavailability of components, there is a need to use average resolutiondigital devices of 10 to 12 bits and at the same time increase theresolution of the commanded force signals. However, conventional ways ofprocessing digital device output, and of performing the aboveconversions, for example, in the processing of the above-describedpressure, area and force values, are in part based on use of the lessavailable, high resolution digital devices, for example.

[0016] What is needed then, is a CMP system in which the accuracy ofpressure and force command signals exceeds the resolution of mechanicalactuating devices and which is less dependent on the use of highresolution, less available, components such as high resolution digitaldevices. In the required CMP system, such need is for a way to moreaccurately compute the value of forces to be applied to a wafer carrier,for example, as a polishing pad moves laterally relative to such wafercarrier during the CMP operation, wherein such computational accuracydoes not depend on the use of high resolution digital devices. Moreover,such improved accuracy should be achieved even though the computationinvolves both digital and analog operations. Further, this improvedcomputational accuracy should be achieved even though it may benecessary to convert values of required pressure or force, for example,from one set of units to a second set of units and then back to thefirst set of units. In such conversion, a value of a required pressure,for example, in the first set of units should have the same value afterthe conversion as before the conversion. In another sense, then, what isneeded are methods and apparatus for quantization, which are effectivewithout the use of high resolution digital devices, and in which theresulting average computational resolution is of less importance inobtaining computed results having an acceptable accuracy, such thatquantization errors are eliminated or significantly reduced.

SUMMARY OF THE INVENTION

[0017] Broadly speaking, the present invention fills these needs byproviding CMP systems in which the accuracy of pressure and forcecomputations is less dependent on the use of high resolution, lessavailable components, such as high resolution digital devices such asdigital to analog converters and analog to digital converters. The CMPsystem of the present invention provide a way to more accurately computethe values of forces to be applied to a wafer carrier, for example, as apolishing pad moves laterally relative to such wafer carrier during theCMP operation. Such computational accuracy does not depend on the use ofhigh resolution digital devices. Moreover, such improved accuracy isachieved even though the computation involves both digital and analogoperations, and even though it may be necessary to convert values ofrequired pressure or force, for example, from one set of units to asecond set of units and then back to the first set of units. In suchconversion, a pressure value, for example, in the first set of units mayhave the same value after the conversion as before the conversion. Thepresent CMP system enables a quantization process to be performedwithout the use of data from high resolution digital devices, and inwhich an average computational resolution is of less importance inobtaining computed results having an acceptable accuracy, such thatquantization errors are eliminated or significantly reduced.

[0018] One aspect of the present invention relates to reducingquantization error in specifying CMT pressure in which a computationalresolution is to be used in processing a required value of the pressureto obtain a computed value of the required pressure. Apparatus isprovided for defining a relatively average value of the computationalresolution (e.g., 10 to 12 bits), and for defining a set of values ofpressure. The set contains possible values of the pressure, includingthe required value of the pressure. The highest value of pressure of theset is divided by the value of the computational resolution to obtain aseries of pressure scales of the set. The pressure scales representuniformly increasing possible values of the pressure, and the scaleshave equal ranges of pressure, each of which ranges has a value inexcess of the value of the required pressure. A different firstidentifier is provided for each of the scales of the pressure, and thenumber of different first identifiers is equal to the value of thecomputational resolution. The required value of the pressure isspecified by providing a different second identifier to indicate a setpoint value within any specific one of the scales. The set pointcorresponds to any particular pressure value. The number of differentsecond identifiers is equal to the value of the computationalresolution.

[0019] Yet another aspect of the present invention relates to moreaccurately representing, for computational processing, a required valueof a variable parameter, the value being among a range of parametervalues. A system component, such as a digital device, is selected andhas an operational resolution defined in terms of a number ofincrements. A computational signal range of a computational signal isdefined to represent the amount by which the required values of theparameter may vary in the parameter range. A processor is programmed todivide the computational signal range by the number of increments of theoperational resolution to represent a plurality of scales within theparameter range, each of the scales having a given number of units perincrement , the number of scales being about equal to the number ofincrements. One of the scales is selected and includes a set point thatidentifies the required value of the parameter, the selected scalehaving a scale range of units. The selected scale is represented interms of a first output signal that is within the computational signalrange, and the set point is represented in terms of a second outputsignal that is within the computational signal range.

[0020] A further aspect of the present invention relates to reducingquantization error in a computation by defining synchronization data forsynchronizing computational operations of first and second digitalprocessors. The computational operations are performed on datarepresenting a parameter. Based on the synchronization data, first andsecond data converting operations are performed by the first digitalprocessor. The first data converting operation converts an initial valueof the parameter to first digital data corresponding to one scale of aplurality of scales in a scale function. The one scale identifies onerange of values of the parameter within an entire set of values of theparameter. The second data converting operation converts the initialvalue to second digital data corresponding to a range function thatidentifies one set point in the one range of values corresponding to thescale. Based on the synchronization data, the second digital processorconverts the first and second digital data to a data item that digitallyrepresents the exact initial value of the parameter.

[0021] An additional aspect of the present invention relates to reducingquantization error in a computation of CMP pressure. The synchronizationdata is defined for synchronizing operations of the first and seconddigital processors. The synchronization data defines a computationalresolution , a set of values of the pressure to be used in computations,a set of values of output pressure data for communications between thefirst and second digital processors, a scale data conversion functionthat defines a relationship between a required polishing pressure andeach one of a plurality of scales into which the set of values of thepressure is divided; and a set point data conversion function thatdefines a relationship between a range of the pressures in a particularone of the scales and a set point that defines one value of the requiredpressure in the particular scale. The first processor performs a firstconversion operation based on the synchronization data. The firstconversion operation is performed on a required value of the pressure,and converts the required value of the pressure to first output pressuredigital data representing a particular one of the scales. The firstdigital processor also performs a second conversion operation based onthe synchronization data. The second conversion operation is performedon the required value of the pressure to convert the required value tosecond output pressure digital data representing the set point thatdefines the required pressure in the particular scale. In the secondprocessor a third conversion operation is performed based on thesynchronization data. The third conversion operation is performed toconvert the first output pressure digital data to scale datarepresenting the particular one of the scales. A fourth conversion isperformed by the second digital processor based on the synchronizationdata. The fourth conversion operation is performed on the second outputpressure digital data to convert the second output pressure digital datato digital data more accurately representing the required value of thepressure.

BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The present invention will be readily understood by the followingdetailed description in conjunction with the accompanying drawings,wherein like reference numerals designate like structural elements.

[0023]FIG. 1A is a schematic elevational view showing a preferredembodiment of the present invention in which a polishing head contacts acontact area of a wafer mounted on a wafer carrier;

[0024]FIG. 1B is a plan view of FIG. 1A, schematically illustrating aninitial position of the polishing head and by dashed lines identifyingan initial contact area between the wafer and a polishing pad on thehead;

[0025]FIG. 1C is a plan view similar to FIG. 1B, illustrating theinitial position of the polishing head and in cross hatch linesidentifying an initial contact area between a retainer ring surroundingthe wafer and the polishing pad on the head, and in dashed-dot linesidentifying an initial contact area between a puck carried by a padconditioner carrier and the polishing pad on the head;

[0026]FIG. 1D is a schematic view of a system of the preferredembodiment of the present invention, wherein a first processor providesfirst inputs to a second processor, the first inputs representing theposition of the polishing pad relative to the wafer, and the secondprocessor being shown receiving second inputs representing the pressureto be applied by the polishing pad on the wafer;

[0027]FIG. 2 is a schematic view of the first digital processor shownoperating based on a recipe and specifying various required CMPpressures;

[0028]FIG. 3 depicts a flow chart illustrating operations of a methodfor specifying the required pressure in terms of a first scaleidentifier specifying a particular scale as the scale in which therequired pressure is located, and a second identifier specifying a valueof a set point within the specified one of the scales;

[0029]FIG. 4 is a schematic view illustrating the scales resulting fromthe method depicted in FIG. 3, and the set point in the specified one ofthe scales;

[0030]FIG. 5 depicts a flow chart illustrating operations of a furthermethod performed in the first digital processor for providing scale andset point signals representing the required pressure to be applied tothe wafer;

[0031]FIG. 6 is a schematic diagram illustrating how to join FIGS. 6Aand 6B;

[0032]FIG. 6A is a schematic diagram of one of two sections of thesecond digital processor that converts pressure request data to apressure request;

[0033]FIG. 6B is a schematic diagram of the second section of the seconddigital processor that converts pressure request data to a forcerequest;

[0034]FIG. 7 depicts a flow chart illustrating operations performed bythe second processor for processing a scale signal and a set pointsignal to define the pressure request;

[0035]FIG. 8 depicts a flow chart illustrating further operationsperformed by the second processor for defining the required force interms of a first scale identifier specifying a particular scale as thescale in which the required force is located, and a second identifierspecifying a value of a set point within the specified one of thescales;

[0036]FIG. 9 is a schematic diagram depicting a set of force scales anda force set point within an identified force scale to represent arequired force;

[0037]FIG. 10 depicts a flow chart illustrating operations performed bythe second digital processor for converting the force scale and forceset point to define the required force in terms of force scale volts andforce set point volts;

[0038]FIG. 11 is a schematic diagram of an analog logic preprocessorthat receives data in terms of the force scale volts and force set pointvolts;

[0039]FIG. 12 depicts a flow chart illustrating operations performed bythe analog logic preprocessor for converting the data in terms of forcescale volts and force set point volts to define a force request;

[0040]FIG. 13 depicts a flow chart illustrating further operationsperformed by the analog logic preprocessor for defining logic and forcerange signals for input to an analog logic processor;

[0041]FIG. 14 is a schematic diagram of the analog processor whichoutputs the required force in terms of one analog voltage to be appliedto a force actuator; and

[0042]FIG. 15 depicts a flow chart illustrating operations performed bythe analog logic processor for defining the value of the one analogvoltage to be applied to the force actuator.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0043] An invention is described for a CMP system that providessolutions to the above-described problems. Such CMP systems render theaccuracy of CMP-related computations less dependent on the use of lessavailable, high resolution components, such as high resolution digitaldevices. Such CMP system of the present invention provides a way to moreaccurately compute values of required pressure and forces to be appliedto a wafer carrier, for example, as a polishing pad moves laterallyrelative to such wafer carrier during the CMP operation. Such CMP systemenables a quantization process to be performed without the use of highresolution components, so that a resulting average computationalresolution is of less importance in obtaining computed results having anacceptable accuracy. As a result, quantization errors are eliminated orsignificantly reduced.

[0044] In the following description, numerous specific details are setforth in order to provide a thorough understanding of the presentinvention. It will be understood, however, to one skilled in the art,that the present invention may be practiced without some or all of thesedetails. In other instances, well known process operations and structurehave not been described in detail in order not to obscure the presentinvention.

[0045] Referring to FIGS. 1A-1D, there is schematically shown apreferred embodiment of the present invention, including a system 200having a resolution enhancement feature for improving the accuracy ofconversion of required chemical mechanical polishing (CMP) pressure P toforce F to be applied by a CMP head 202 to a wafer 204, for example.Generally, the system 200 may use an encoder 208 (FIG. 1D), to provideencoder signals 210 indicating the position of the CMP head 202 relativeto the wafer 204. The system 200 may also use a processor 212, such as apersonal computer, to process a recipe 213 that specifies the operationsof the system 200 for required processing of the wafer 204, e.g., forCMP operations. The processor 212 may be a personal computer having arated processing capacity of a 600 MHz Pentium TM series processor, orequivalent., and running under an NT O/S and under a visual logiccontroller program (VLC) sold by Steeplechase, for example. Theprocessor 212 may output separate signals 214, 216, and 218 representingindividual required pressures P that are required to be applied by apolishing, or planarization, pad 220. For example, signals 214 representvalues of one such pressure Pwp to be applied by the pad 220 on thewafer 204. Signals 216 represent values of another such pressure Pcp tobe applied by the pad 220 on a conditioner puck 222. Signals 218represent values of the other such pressure Pwp to be applied by the pad220 on a retainer ring 224. Use of the letter “P” refers generally tosuch required pressures, and is shown in FIG. 1D. Reference to aspecific one of the required pressures P is indicated by the use of Pwp,Pcp, or Prp. The term “Pressure Profiles” shown in FIG. 1D indicatesthat the recipe 213 may specify that the value of any such pressure P isto be constant, or that such value is to vary over time.

[0046] To illustrate the present invention, a situation is described inwhich the value of the pressure P is to be constant, and in which thehead 202 and the pad 220 may move relative to each of the wafer 204, thepuck 222, and the ring 224 (see arrow 226 in FIG. 1A). Of course, thepressure P may vary in the operation of the system 200. In the exemplaryconstant pressure situation, the relative motion results in changingvalues of areas AW (FIG. 1B), and AC and AR (shown in FIG. 1C) ofoverlap (or contact) of the pad 220 on (or with) the respective wafer204, puck 222, and ring 224. The pressure P is in terms of the force Fapplied to an area A. With the values of the respective pressures Pwp,Pcp, and Prp maintained constant in this example, as the pad 220 movesin the directions of the arrow 226, the values of the respective forcesFwp, Fcp, and Frp applied to respective areas Awp, Acp, or Arp mustchange in proportion to the changes in the values of the respective areaAW, AC, or AR. The term “Force Profiles” shown in FIG. 1D indicates thatin response to the recipe 213 specifying a value of any such pressure P,the corresponding value of the force F (e.g., Frp, Fcp, or Fwp) may varyover time. The encoder signals 210 and the pressure signals 214, 216,and 218 are applied to a multi-axis force controller 228, wherein oneaxis is for the wafer 204, another axis is for the puck 222, and theother axis is for the ring 224. The force controller 228 may be aprogrammable signal processor (DSP) sold by Logosol, Inc. and having aper axis processing capacity of about that of a 486 series Intel TMprocessor or equivalent. Such processor 228 has three axes, onecorresponding to each of the three axes described above, such that thethree axes may be processed at the same time.

[0047] The wafer axis of the controller 228 processes the encoder signal210 in respective area processors 230W for the area Awp, 230C for thearea Acp, and 230R for the area Arp. Respective signals 232W, 232C, and232R represent the respective areas Awp, Acp, and Arp at a moment oftime and corresponding to the particular relative position of the pad220 and the respective wafer 204, puck 222 and ring 224. The respectivesignals 232W, 232C, and 232R are applied to respective force processors234W, 234C, and 234R which convert the respective pressure signals 214,216, and 218 and the respective area signals 232W, 232C, and 232R torespective signals 236W, 236C, and 236R representing the respectiveforces Fwp, Fcp, and Frp in terms of force units such as pounds, forexample. The signals 236W, 236C, and 236R are applied to an analog logicprocessor 237 having a section corresponding to each of the signals236W, 236C and 236R. The respective sections of the analog logicprocessor 237 provide respective force signals 238W, 238C and 238R torespective force actuators 239W, 239C, and 239R (FIG. 1A) which urge therespective wafer 204, puck 222, and ring 224 toward the pad 220 to applyrespective required pressure Pwp, Pcp, and Prp to the respective wafer204, puck 222, and ring 224. As described above, the force actuators 239may be of the high resolution type, such as linear electromagneticactuators, rather than the low resolution pneumatic actuators notedabove.

[0048] The processor 212, the force controller 228, and the analog logicprocessor 237 are configured to minimize, if not eliminate, theabove-defined quantization error. In the context of the system 200, theabove-defined term “quantization” refers to the below-described processof computation performed by the processor 212, the force controller 228,and the analog logic processor 237, in which computational resolution isof significant importance in obtaining the values of the respectiveforces Fwp, Fcp, and Frp computed results, each of which has anacceptable accuracy.

[0049] In a quantization process performed with respect to one of theaxes, a parameter may be the required pressure P, such as the requiredpressure Pwp, for example. Other quantization processes may be performedwith respect to the other two axes (puck and ring), and the parametersmay be the respective required pressures Pcp and Prp having appropriateinitial values. Using the required pressure Pwp as an example forpurposes of description of all such required pressures Pwp, Pcp, andPrp, such exemplary pressure Pwp may have an initial value of 0.005 psi,for example. Such initial value of the exemplary required pressureparameter Pwp is subjected to the below-described computationaloperations in the processor 212, the force controller 228, and theanalog logic processor 237 to obtain the computed result, which is thevalue of the force Fwp corresponding to the initial value of thepressure Pwp. Similar operations with respect to the other requiredpressures Pcp and Prp result in obtaining the value of the requiredrespective forces Fcp and Frp as the respective computed results.

[0050] Such quantization process may be performed with minimum, or no,quantization error, as defined above, even though the system 200includes digital devices such as the force controller 228, for example,having the relatively average component resolution defined below andeven though the computations in the processor 212, the force controller228, and the analog logic processor 237 are based on an averagecomputational resolution. A preferred value of the selected componentresolution is about six bits, and a more preferred value of thecomponent resolution is about eight bits, and a most preferred value ofthe component resolution is from about ten to twelve bits. Thecomponents in the high end of this range are referred to as having a“relatively average” component resolution, which is in comparison todigital devices having high resolutions of from about fourteen bits toabout 16 bits, for example. As described above with respect to componentavailability, digital devices having relatively average resolution arereadily available, whereas as resolution increases such high resolutiondigital devices are less available.

[0051] The recipe 213 typically specifies a preferred range of requiredpressure P of from about zero psi to about ten psi. However, without thebenefits of the present invention, the low end of the range is generallya pressure of about 1.5 psi. With the present invention, the range ofthe pressure P may start from about zero psi. The parameter resolution(as defined above) of the preferred pressure range is 0.001 psi, forexample, which is to say that the required pressure Pwp is mostpreferrably specified in increments or steps of 0.001 psi.

[0052] With such parameter resolution and component resolution in mind,for comparative purposes the normal criteria described above may be usedas follows to determine whether quantization error would normally resultfrom the use of the selected relatively average component resolution of10 bits (or 1024 counts), i.e., without the present invention. Theexemplary absolute value of the parameter (pressure) increment is 0.001psi. The absolute value of computational pressure range steps isdetermined by the pressure range of 10 psi divided by 1024 (i.e., about0.01 psi per step). Thus, the absolute value of the parameter resolutionincrement is much less than the absolute value of the pressure rangestep. Based on the above normal criteria, one would expect significantquantization error to result because a choice of zero or 0.01 psi wouldbe available as the steps closest to the required exemplary 0.005 psipressure Pwp. Each of such steps of the choice would have an error of0.005 psi, or 100%. However, as described below, such quantization errordoes not occur in the use of the present invention. Rather, with the tenor twelve bit component resolution of the described digital devices(e.g., the force controller 228) and the same computational resolution,no quantization error should result.

[0053] In FIG. 1D, the processor 212, the force controller 228, and theanalog logic processor 237 are shown as separate units. To achieve therequired minimization or elimination of the quantization error, thepresent invention includes a method of specifying the chemicalmechanical polishing pressure P (the pressure profiles in FIG. 1D, forexample). The method facilitates improvements in communicating the valueof the exemplary required pressure Pwp from the processor 212 to theforce controller 228, and from the force controller 228 to the analoglogic processor 237, and to the force actuators 239. Referring to FIGS.2 and 3, the processor 212 is programmed by an instruction 240. Themethod is defined by a flow chart 242 depicted in FIG. 3, and startswith an operation 244 implementing the instruction 240. Operation 244outputs the exemplary required pressure Pwp (0.005 psi) as a pressurerequest 246. The method moves to an operation 248 for specifying the 10bit computational resolution to be used in processing to obtain acomputed value of the required pressure Pwp. The computed value is tohave improved accuracy. In FIG. 1D a keyboard 250 or other input deviceis provided for performing operation 248. The method moves to anoperation 252 for defining the set of values representing the range ofpossible required pressures Pwp . The set includes the required value(0.005 psi) of the exemplary pressure Pwp. The method moves to anoperation 254 to implement instruction 256. Operation 254 divides thehighest value (10 psi) of the exemplary range of possible requiredpressure Pwp by the value of the computational resolution (the exemplary1024) to obtain a series of pressure scales 258. The pressure scales 258may be identified by 0-L1, L1-L2, . . . (Ln-1)-Ln, as shown in FIG. 4,for example. The pressure scales 258 represent ranges 260 of uniformlyincreasing possible values of the exemplary pressure Pwp, where theranges 260 have equal amounts of the required pressure Pwp. In theexemplary situation, each of the ranges 260 equals 0.01 psi. A differentfirst scale identifier (e.g., “I1”, “I2”, . . . “In”) is provided foreach of the scales 258 of the exemplary range of pressure Pwp. A number(the exemplary 1024) of different first identifiers “In” is equal to thevalue of the computational resolution (the exemplary 1024). In theexample, operation 254 results in the first scale identifier specifyingscale I1 as the scale in which the required exemplary pressure Pwp islocated.

[0054] The instructions 256 are further implemented as the method movesto an operation 264 for specifying the required value (the exemplary0.005 psi) of the pressure Pwp by providing a different secondidentifier (SP) to indicate a value of a set point 266 within anyspecific one of the scales 258, e.g. scale Ii. The set point 266 maycorrespond to any particular pressure value in the identified scale 258,e.g. 0.005 psi in scale I1. The number of different second identifiersSP (the exemplary 1024) is equal to the value of the computationalresolution (the exemplary 1024 in the exemplary situation). The setpoint 266 corresponding to the pressure Pwp is identified by the secondidentifier SP512 in FIG. 4. In FIG. 3 the specifying of the exemplaryCMP pressure Pwp is completed as operations 254 and 264 output therespective first and second identifiers I1 and SP512. It may beunderstood that the computational resolution is used to obtain each ofthe scale identifier and the set point identifier. In other words, eachof the scales 258 is divided into the exemplary 1024 possible setpoints.

[0055] Referring to FIGS. 2 and 5, other instructions are processed bythe processor 212, including instruction 270, 272, 274, 276, 278, and280, which are implemented by operations of a flow chart 284 shown inFIG. 5 for communicating the specific required value of the exemplarypressure Pwp to the force controller 228 for more accurate processing ofthe required value of the exemplary pressure Pwp. Operation 286implements a pressure scale-to-count conversion of instruction 270, bywhich the exemplary first identifier “In” is converted to a number ofcounts. For example, the exemplary identifier I1 representing the firstscale 258 is represented by 1 count. The identifier In representing thelast scale 258 would be represented by the exemplary 1024 countscorresponding to an appropriate value of the pressure Pwp. The methodmoves to operation 288 which implements a pressure set point-to-countconversion of instruction 272, by which the second identifier SP512 isconverted to a number of counts. For example, the exemplary identifierSP512 representing the set point 266 is represented by 512 counts tocorrespond to the value of 0.005 psi which is one-half way between 0.00psi and 0.01 psi. An exemplary identifier SP1024 would identify the lastset point 266 and would be represented by 1024 counts. For efficiency ofoperation of the force actuators 239, the pressure scale-to-countconversion provides count values of between 0 and 1024 for the oddnumbered pressure scales 258 (e.g., scales I1, I3, etc.) whereas thecount values of the even numbered pressure scales 258 are between 1024and 0.

[0056] The method moves to operations 290 and 292 which respectivelyimplement instructions 274 and 276 to collectively generate one of thesignals 214 when pressure Pwp is processed, or the respective signals216 and 218 when the respective pressure Pcp or Prp are processed. Eachsuch signal is in two parts. In the exemplary situation, one partrepresents the required value (0.005 psi) of the exemplary pressure Pwpin terms of a pressure scale part 214S, and a second part represents apressure set point part 214SP. Operation 290 implements a pressure scalecount-to-voltage conversion of instruction 274. The implementation inoperation 290 again uses the computational resolution, by which thecount value of the first identifier “I1” is converted to a voltage. Theconversion is performed by selecting a value of a range of voltage ofthe output 214, such as 10 volts. The voltage range is divided by thecomputational resolution to obtain a value of a pressure scale dataconversion function, which in the exemplary situation is 0.01 volts percount. The one count value of the first scale identifier I1 thuscorresponds to a 0.01 volt value, which may be referred to as pressurescale volts and represents the value of the pressure scale part 214S ofthe two part signal 214.

[0057] The method moves to operation 292 that implements a pressure setpoint count-to-voltage conversion of instruction 276. The implementationin operation 292 again uses the computational resolution, by which thecount value of the second identifier “SP512” is converted to a voltage.The above 10 volt value of the range of the signal 214 divided by thecomputational resolution provides a pressure set point data conversionfunction having a value of about 0.01 volts per count. The 512 countvalue of the second scale identifier SP512 thus corresponds to about a5.0 volt value, which may be referred to as pressure set point volts andrepresents the value of the pressure set point part 214SP of the twopart signal 214.

[0058] The method moves to operation 294 to implement instructions 278and 280. The exemplary required pressure Pwp is defined in terms of thesignal 214S (i.e., the 0.01 volt value of the pressure scale volts) andthe signal 214SP (i.e., the 5.0 volt value of the pressure set pointvolts). The method is then done. As shown in FIG. 2, the signals 214Sand 214SP are output from the processor 212, and are applied to theforce controller 228 shown in FIG. 6A. The methods of flow charts 242and 284 facilitate improved accuracy of communication of the value ofthe exemplary required pressure Pwp from the processor 212 to the forcecontroller 228, in that, as described below, the exact value of theexemplary required pressure Pwp may be obtained in the force controller228.

[0059] One aspect of the improved accuracy of communication of the valueof the exemplary required pressure Pwp from the processor 212 to theforce controller 228 is facilitated by defining synchronization, orpressure synchronization, data 300. This data 300 synchronizes thecomputational operations of the processor 212, which represents a firstdigital processor, and of the force processor 234W of the controller228, which represents a second digital processor. The synchronizationdata 300 includes the data set forth in Table I: TABLE I SYNCHRONIZATIONDATA 300 The computational resolution The set of values representing therange of possible required pressures P The definition of the pressurescales 258 The pressure scale data conversion function The pressure setpoint data conversion function

[0060] As described above, the operations in flow charts 242 and 284 arebased on one or more items of the synchronization data 300. Theprocessor 212 and the force controller 228 are provided with thesynchronization data 300 from a hard drive 301, for example, via a bus296. The data 300 is in the form of an RS232 signal applied to the forcecontroller 228, for example. In general, based on one or more items ofthe synchronization data 300, the second digital processor (i.e., theforce processor 234W, FIG. 1D) converts first and second digital data(e.g., the exemplary respective 0.01 volt signal 214S and the exemplary5 volt signal 214SP) to one data item 302, which is a pressure requestthat ideally digitally represents the exact initial value (e.g., theexemplary 0.005 psi) of the parameter (the exemplary required pressurePwp).

[0061] In more detail, FIGS. 6A and 6B taken together show the forceprocessor 234W as being provided with the synchronization data 300(shown as the RS232 signal) from the hard drive 301 via the bus 296. Theforce processor 234W includes instructions 304, 306, and 308 forprocessing the signal 214S, and instructions 310, 312, and 308 forprocessing the signal 214SP. FIG. 7 shows a flow chart 320 depictingoperations for processing the signal 214S. An operation 322 converts thevalue of the voltage of the pressure scale signal 214S to digital data324 representing counts and having a value corresponding to therespective exemplary specified pressure scale I1, i.e., 1 count. In suchconversion, operation 322 uses the pressure scale data conversionfunction of the synchronization data 300. The method moves to operation326 in which instruction 306 is processed to convert the 1 count valueof the digital data 324 to digital data 328 representing the one of the1024 scales shown in FIG. 4. In such conversion, operation 326 uses thedefinition of the scales 258 of the synchronization data 300.

[0062] When the method moves to operation 322, the method also moves tooperation 330 for converting the value of the voltage of the pressureset point signal 214SP to digital data 332 representing counts andhaving a value corresponding to the respective specified scale SP512,i.e., 512 counts. In such conversion, operation 330 uses the pressureset point data conversion function of the synchronization data 300. Themethod moves to operation 334 in which instruction 312 is processed toconvert the 512 count value of the digital data 332 to digital data 336representing the set point in scale I1 shown in FIG. 4. In suchconversion, operation 326 uses the definition of the scales 258.

[0063] The method moves to operation 338 in which instruction 308 isprocessed to convert the exemplary pressure scale I1 identityrepresented by the digital data 328, and the pressure set point identityrepresented by the data 336. Conversion of the pressure scale I1 resultsin an identification of value of the range (zero to 0.01 psi) of the oneof the 1024 scales described in FIG. 4 that includes the exemplarypressure Pwp. Conversion of the set point SP512 results in identifyingthe exact value of the exemplary required pressure Pwp, i.e., 0.005 psi.In such conversion, operation 338 uses the definition of the pressurescales 258 of the synchronization data 300. Digital data 340representing the value (the exemplary 0.005 psi) of the requiredpressure Pwp is output as the pressure request 302.

[0064] Reference to FIGS. 2, 6A and 6B indicates that theabove-described use of the pressure synchronization data 300 in theforce processor 234W, the selection of the relatively averagecomputational resolution, and the dividing of such computationalresolution into both the pressure range of the exemplary requiredpressure Pwp and the voltage range of the output signals 214,facilitates the improved accuracy of the communication of the value ofthe exemplary required pressure Pwp from the processor 212 to the forceprocessor 234W.

[0065] As described above, the encoder signals 210 and the pressuresignals 214, 216, and 218 are applied to the force processor 234W of themulti-axis force controller 228. The force controller 228 may be aprogrammable signal processor (DSP) sold by Logosol, Inc. and having aper axis processing capacity of about that of a 486 series Intel™processor or equivalent. This DSP processor 228 has three axes, whichmeans that the three axes (each of the wafer 208, the ring 226 and thepuck 222) may be processed at the same time. FIGS. 6A and 6B takentogether show the details of the force processor 234W for the one waferaxis. FIGS. 7 and 8 show operations of methods performed by the forceprocessor 234W. The details for the two other axes and the methodoperations for such axes are similar to those shown in FIGS. 6A, 6B, 7and 8.

[0066] The wafer axis of the processor 234W shown in FIGS. 6A and 6Bprocesses the encoder signal 210 in the area processor 230W to definethe area Awp at a moment of time and corresponding to the particularrelative position of the pad 220 and the respective wafer 204. It isunderstood that the resolution of the encoder 208 is high enough as toinduce only small errors in such defining of the areas A. Thisprocessing is described in the Prior Application, and results in thesignal 232W being applied to the force processor 234W of the forcecontroller 228. FIGS. 6A and 6B show the pressure request 302 and thearea signal 232W input to a force calculation instruction 350. Theinstruction 350 is processed as also described in the Prior Application,and results in a force request 352. The force request 352 may be interms of digital data 354 representing the force in force units such aspounds corresponding to the exemplary required pressure Pwp to beapplied to the exemplary area Awp.

[0067] To achieve the required minimization or elimination of thequantization error, the present invention further includes a method ofspecifying the CMP force F (the force profiles in FIG. 1D, for example).The method facilitates improvements in communicating the value of theexemplary force Fwp (corresponding to the required pressure Pwp) fromthe force controller 228 to the analog logic preprocessor 237PP shown inFIG. 11. Referring to FIGS. 6A, 6B, 8 and 9, the force processor 234W isprogrammed by instructions 360. The method is defined by a flow chart362, and starts with an operation 364. Operation 364 outputs anexemplary required force Fwp (7.5 pounds) representing the force request352. The method moves to an operation 368 for specifying a computationalresolution (e.g., the average 10 or 12 bit computational resolution) tobe used in processing to obtain a computed value of the force Fwp. Thecomputational resolution (e.g., 10 bits) is read from the pressuresynchronization data 300 stored in the drive 301. The method moves to anoperation 370 for defining the set of values representing the range ofpossible required force. The set includes the required value (exemplary7.5 pounds) of an exemplary force Fwp. Processing of forces Fcp and Frpis performed in a manner similar to that described below with respect tothe force Fwp.

[0068] The method moves to an operation 372 to further implement theinstruction 360. Operation 372 divides the highest value (about 1000pounds) of the exemplary range of possible required force Fwp by thevalue of the computational resolution (the exemplary 1024) to obtain aseries of force scales 376. The force scales 376 may be identified by0-M1, M1-M2, . . . (Mn-1)-Mn, as shown in FIG. 9, for example. The forcescales 376 represent ranges 378 of uniformly increasing possible valuesof the exemplary force Fwp, where the ranges 378 have equal amounts offorce. In the exemplary situation, each of the ranges 378 equals about 1pound. A different first scale identifier (e.g., “II1”, “II2”, -“IIn”)is provided for each of the force scales 376 of the exemplary force Fwp,and a number (the exemplary 1024) of different first identifiers “IIn”is equal to the value of the computational resolution (the exemplary1024). In the example, operation 372 results in the first scaleidentifier specifying scale II8 as the force scale in which theexemplary required force Fwp is located.

[0069] The instructions 360 are further implemented as the method movesto an operation 380 for specifying the required value (the exemplary 7.5pounds) of the force Fwp by providing a different second identifier(SSP) to indicate a value of a set point 382 within any specific one ofthe scales 376, e.g. the exemplary force scale II8. The force set point382 may correspond to any particular force value in the identified forcescale 376, e.g. the exemplary 7.5 pounds in scale II8. The number ofdifferent second identifiers SSP (the exemplary 1024) is equal to thevalue of the computational resolution (1024 in the exemplary situation).The force set point 382 corresponding to the force Fwp is identified bythe second identifier SSP512 in FIG. 9. In FIG. 8 the specifying of theexemplary CMP force Fwp is completed as operations 372 and 380 outputthe respective first and second identifiers II8 and SSP512.

[0070] Referring to FIGS. 6A, 6B, and 10, other instructions areprocessed by the force processor 234W, including instructions 400, 402,404, 406, 408, and 410 which are implemented by operations of a flowchart 412 for communicating the specific required value of the exemplaryforce Fwp to the analog logic preprocessor 237PP for more accurateprocessing of the required value of the exemplary force Fwp. The analoglogic preprocessor 237PP may be a programmable signal processor (DSP)sold by Logosol, Inc. and having a per axis processing capacity of aboutthat of a 486 series Intel™ processor or equivalent, similar to thatused for the force controller 228. In FIG. 10 operation 414 is shown forimplementing a force scale identifier-to-count conversion of instruction400, by which the first identifier “IIn” is converted to a number ofcounts. For example, the exemplary identifier II8 representing theeighth force scale 376 is represented by 8 counts; and the exemplaryidentifier II1000 representing the last force scale 376 is representedby the exemplary 1024 counts. The method moves to operation 416 whichimplements a force set point identifier-to-count conversion ofinstruction 406, by which the second identifier SSP is converted to anumber of counts. For example, the exemplary identifier SSP512representing the set point 382 is represented by 512 counts tocorrespond to the value of 7.5 pounds being one-half way between 7.0pounds and 8.0 pounds. For efficiency of operation of the forceactuators 239, the scale-to-count conversion provides count values ofbetween 0 and 1024 for the odd numbered force scales 376 (e.g., scalesI1, I3, etc.) whereas the count values of the even numbered force scales376 are between 1024 and 0.

[0071] The method moves to operations 418 and 420 which respectivelyimplement instructions 402 and 408 to collectively generate one of thesignals 236W, 236C, and 236R in the form of two parts. In the exemplarysituation relating to signal 236W, one part represents the requiredexemplary value (7.5 pounds) of the exemplary force Fwp in terms of aforce scale part 236S and a force set point part 236SP. In more detail,the method moves to operation 418 which implements a force scalecount-to-voltage conversion of instruction 402. The implementation inoperation 418 again uses the computational resolution, by which thecount value of the first identifier “IIn” is converted to a voltage. Theconversion is performed by selecting a value of a range of voltage ofthe output 236W, such as 10 volts. The voltage range is divided by thecomputational resolution to obtain a value of a force scale dataconversion function, which in the exemplary situation is 0.01 volts percount. The eight count value of the first scale identifier II1 thuscorresponds to a 0.08 volt value, which may be referred to as forcescale volts and represents the value of the force scale part 236S of thetwo part signal 236.

[0072] The method moves to operation 420 that implements a force setpoint count-to-voltage conversion of instruction 408. The implementationin operation 420 again uses the computational resolution, by which thecount value of the second identifier “SSP512” is converted to a voltage.The above exemplary 10 volt value of the range of the signal 236SPdivided by the computational resolution provides a force set point dataconversion function having a value of 0.01 volts per count. The 512count value of the second scale identifier SSP512 thus corresponds to a5.0 volt value, which may be referred to as force scale volts andrepresents the value of the force set point part 236SP of the two partsignal 236.

[0073] The method moves to operation 422 in which the exemplary requiredforce Fwp is defined in terms of the signal 236S (i.e., the 0.08 voltvalue of the force scale volts) and the signal 236SP (i.e., the 5.0 voltvalue of the scale volts). The method is then done. As shown in FIGS. 6Band 11, the signals 236S and 236SP are communicated from the forcecontroller 228 to the analog logic preprocessor 237PP. The methods offlow charts 362 and 412 facilitate improved accuracy of communication ofthe value of the exemplary required force Fwp from the force processor234W to the analog logic preprocessor 237PP, in that, as describedbelow, the exact value of the exemplary required force Fwp may beobtained in the analog logic preprocessor 237PP.

[0074] Consistent with the use of the pressure synchronization data 300for communications between the processor 212 and the force processor234W, communications between the force processor 234W and the analoglogic preprocessor 237PP are synchronized by analog synchronization data431 described below. This data 431 synchronizes the computationaloperations of the force processor 234W, which represents a first digitalprocessor, and of the analog logic preprocessor 237PP, which representsa second digital processor. FIGS. 6A and 6B show the force processor234W as being provided with the analog synchronization data 431 from thehard drive 301 via the bus 296 in the form of the RS232 signal. Theanalog synchronization data 431 includes the data set forth in Table II:TABLE II ANALOG SYNCHRONIZATION DATA 431 The computational resolutionThe set of values representing the range of possible required force FThe definition of the force scales 376 The force scale data conversionfunction The force set point data conversion function

[0075] As described above, the operations in flow charts 362 and 412 arebased on one or more items of the analog synchronization data 431.Similarly, in general, based on one or more items of the analogsynchronization data 431, if the force processor 234W is considered afirst digital processor, then a second digital processor in the form ofthe analog logic preprocessor 237PP converts first and second digitaldata (the exemplary respective 0.08 volt signal 236S and the exemplary 5volt signal 236SP) to one data item, which is a force request 450 (FIG.11) that ideally digitally represents the exact initial value (7.5pounds) of a parameter (the exemplary required force Fwp). In moredetail, FIG. 11 shows the analog logic preprocessor 237PP as beingprovided with the analog synchronization data 431 (in the form of theRS232 signal) from a hard drive 432 via the bus 430. FIG. 11 also showsthe analog logic preprocessor 237PP as including instructions 452 and454 for processing the force scale signal 236S, and instructions 456 and458 for processing the signal 236; along with instructions 460. FIG. 12shows a flow chart 462 depicting operations for processing the signal236S. An operation 464 converts the value of the voltage of the forcescale signal 236S to digital data 466 representing counts and having avalue corresponding to the respective exemplary specified force scaleII8, i.e., 8 counts. In such conversion, operation 464 uses the forcescale data conversion function of the analog synchronization data 431.The method moves to operation 468 in which instruction 454 is processedto convert the exemplary 8 count value of the digital data 466 todigital data 470 representing the one of the 1024 scales 376 identifiedas the exemplary force scale 118 in FIG. 9. In such conversion,operation 468 uses the definition of the scales 376 of the analogsynchronization data 431.

[0076] When the method moves to operation 464, the method also moves tooperation 470 for converting the value of the voltage of the signal236SP to digital data 472 representing counts and having a valuecorresponding to the respective specified scale SSP512, i.e., 512counts. In such conversion, operation 470 uses the force set point dataconversion function of the synchronization data 431. The method moves tooperation 474 in which instruction 458 is processed to convert the 512count value of the digital data 472 to digital data 476 representing theforce set point in scale II8 shown in FIG. 9. In such conversion,operation 474 uses the definition of the force scale 376.

[0077] The method moves to operation 478 in which instruction 460 isprocessed to convert the force scale II8 identity represented by thedigital data 470, and the force set point identity represented by thedata 476 to an identification of the value of the range (7.0 to 8.0pounds) of the one force scale 376 shown in FIG. 9 that includes theexemplary force Fwp. Conversion of the force set point SSP512 results inidentifying the exact value of the exemplary required force Fwp, i.e.,7.5 pounds. In such conversion, operation 478 uses the definition of theforce scales 376 of the analog synchronization data 431. Digital data480 representing the exemplary required force Fwp is output as thepressure request 450.

[0078] Reference to FIGS. 6A, 6B, and 11 indicates that theabove-described use of the analog synchronization data 431 in the analoglogic preprocessor 237PP, the selection of the relatively averagecomputational resolution, and the dividing of such computationalresolution into both the force range of the exemplary required force Fwpand the voltage range of the output signals 236S and 236SP, facilitatesthe improved accuracy of the communication of the value of the exemplaryrequired force Fwp from the force processor 234W to the analog logicpreprocessor 237PP.

[0079]FIG. 11 further shows that the analog logic preprocessor 237PP isalso provided with instructions 500 for converting the force request 450into an analog upper range signal 502 and an analog lower range signal504, and to two digital logic signals 506 and 508. The instructions 500are implemented by a method depicted by a flow chart 510 shown in FIG.13. An operation 512 uses the force scale 376 and the exemplary forceidentifier II8 to cause the signals 502 and 504 to define, or represent,the respective upper and lower boundaries, or range, of the one forcescale 376 identified by the exemplary identifier II8. Thus, the signal502 represents 8 volts and the signal 504 represents 7 volts in theexemplary situation in which the exemplary required force F is to be 7.5pounds. The method moves to operation 514 which defines digital logicfor identifying the set point 382 within the identified force scale 376,and the method is done. The digital logic is based on the computationalresolution (e.g., 10 bits in the exemplary situation).

[0080] For ease of description, FIG. 14 primarily shows an example of 2bit logic of the signals 506 and 508, and the following descriptionrefers to how the 2 bit logic and the 10 bit logic are implemented. FIG.14 schematically depicts analog circuitry 511 for converting the fourinput signals 502, 504, 506, and 508 to one of the analog signals 238,in this case the exemplary analog signal 238W shown in FIG. 1D. A methodof operation of the circuitry 511 is shown on FIG. 15 which depicts aflow chart 550. In an operation 552 the range signals 502 and 504 areapplied to a subtractor circuit 520 to generate an analog range-of-forcesignal 522 representing the difference between the values of the signals502 and 504. In the exemplary situation, the value of the difference is1 volt, which is the value of the analog range-of-force signal 522.Based on the resolution of the digital logic signals 506 and 508, whichin the example of FIG. 14 is 2 bits, in an operation 554 a dividercircuit 524 converts the value of the analog range-of-force signal 522(i.e., the difference between the two analog force signals 502 and 504)to an analog force increment signal 526, representing a value of 0.25volts in the exemplary situation. The resolution (e.g., 2 bit) input tothe divider circuit 524 may, for example, be from the drive 432 and isbased on the analog synchronization data 431. An input to the divider524 is provided by a divider 527. The divider 527 reduces the value ofthe signals 502 and 504 according to the range of the analog signals238. For example, in the 2 bit situation 2 bits (2×2) is divided by 1;or in the 4 bit situation, 16 is divided by 2; and in the 10 bitsituation 1024 is divided by 100 (which is the exemplary value shown inFIG. 14).

[0081] Based on the logic defined by the two digital logic signals 506and 508 via an analog logic signal 528, a multiplier circuit 530converts the value of the analog force increment signal 526 (theexemplary 0.25 volts) to an analog force set point signal 532. In theexemplary situation the value of the signal 532 is 0.5 volts (0.25 timesthe value 2 of the analog logic signal 528). FIG. 14 shows, andoperation 556 describes, one of the analog force signals 502 and 504 (e.g., the lower signal 504) added to the analog force set point signal 532to determine the value (in this example, 7.5 volts) of the forceactuator signal 238W. In operation 558 the force actuator signal 238W isoutput and has the improved accuracy.

[0082] It may be understood that with the 2 bit logic shown by examplein FIG. 14, only two logic input signals 506 and 508 are used (e.g.,logic A and B). When the noted 10 bit logic is used for the logicsignals, such as 506 and 508, etc., ten such logic signals are used(e.g., logic A-J). The circuitry for the 10 bit logic will be understoodby first referring to the 2 bit logic shown in FIG. 14. An analoganalysis circuit 570 receives the respective A and B logic signals 506and 508. The circuit 570 may be a programmable signal processor (DSP)sold by Logosol, Inc. With the 2 bit logic, two times two, or four,possible logic states 572-575 may be provided by the two input logicsignals 506 and 508. In the 10 bit case, 1024 logic states areachievable with 10 bit logic signals corresponding to logic A throughlogic J. In the 2 bit example, one of the logic states 572-575 outputs alogic signal 590 for any given logic input collectively defined by thesignals 506 and 508. Each logic signal 590 is accompanied by amultiplier input 592 having a one volt value. The value of the signals590 is selected according to the required values of the analog force setpoint signals 532. Generally, the values of the logic signals 590 arewithin the range of a 24 volt power supply. Thus, in the 10 bit example,the values of the logic signals 590 may range from 0.0 volts to about10.0 volts (in the exemplary 0.01 volt increments shown in FIG. 14). Inthe 2 bit example, the signals 590 would be in a range of 0.0 volts to 3volts, for example, in 1.0 volt increments, such that one exemplarysignal 596 could have a 2 volt value.

[0083] The value of the signals 532 in turn depends on the values of thesignals 526 and 528. The corresponding multiplier input 592 and logicsignal 590 are input to a respective corresponding multiplier 594. Forany given logic input to the analog logic evaluation circuit 570, onlyone multiplier 594 outputs a product signal 596 having a value otherthan zero. The product signals 596 are added as shown by staged adders600 to provide a series of sum signals 602, 604, and 528. The value ofthe last sum signal is the value of the analog logical voltage signal528, and depends on the logic input by the signals 506 and 508. In the10 bit logic example, there are 1024 multipliers 594, and 1023 stages ofthe adders 600.

[0084] As an example for the 2 bit logic, with the 7.5 volt value of therequired force Fwp, and the value of 0.25 volts (1 volt divided by 4) ofthe analog force increment signal 526, to obtain the 7.5 volt value, thesum, or analog logical voltage, signal 528 has the value of 2 voltsbased on the 2 volt signal 596 from one of the multipliers 594. 2 voltstimes the increment 0.25 (the exemplary value of the signal 526 in the 2bit example) gives the product 0.5 volts, which corresponds to thevoltage amount above the 7 volt value of the signal 504 corresponding tothe voltage value of 7.5 volts of the required force Fwp. In summary,the number of logic states in the evaluation circuit 570 equals thenumber of multipliers 594, and there is one less adder 600 than thevalue of the computational resolution.

[0085] An example of the exemplary 10 bit logic is as follows when therequired pressure Pwp is the exemplary 0.005 psi, and a correspondingrequired force Fwp is 0.25 pounds for a 200 mm wafer 208, for example.An exemplary voltage range of the signals 236 (FIG. 6B) is 10 volts(which corresponds to a range of 502 pounds of the required force Fwpfor a 10 psi maximum pressure P for the 200 mm wafer 208). The value ofthe inputs 592 may range from zero volts to 10.24 volts in 0.01 voltincrements, and as shown in FIG. 14, the difference between the LRvoltage signal 504 and the UR voltage signal 502 (the value of thesignal 522) may be 9.766 millivolts. The ten logic inputs 506, 508, etc.may thus cause the analog logical voltage signal 528 to change inincrements of 9.537 times 10 to the minus six power. As a result, the LRvoltage 504 may be increased in increments of 9.537 times 10 to theminus six power. Therefore, the double use of the relatively average 10bit resolution results in the signals 238 (e.g., the signal 238W in FIG.14) having a very small incremental value, which significantly improvesthe accuracy of the force signals 238, and importantly may conform theincrements in which the force signals 238 are valued to the incrementsof the high resolution electromagnetic actuators, for example.

[0086] In view of the foregoing description, it may be understood thatin the use of the system 200 the accuracy of computations of thepressure P and the force F are less dependent on the use of highresolution, less available digital devices. The CMP system 200 and thedescribed methods therefore provide a way to more accurately compute thevalues of the forces F that are to be applied to the wafer 204, forexample, as the 220 polishing pad moves laterally (arrow 226, FIG. 1A)relative to such wafer 204 during the CMP operations. Moreover, suchimproved accuracy is achieved even though the computation involves boththe digital operations of the processor 212 and the controller 228, forexample, and the analog operations of the circuitry 511. Importantly,such improved accuracy is achieved even though it may be necessary toconvert values of the required pressure P or force F, for example, fromone set of units to a second set of units and then back to the first setof units. In such conversion, it is seen that a pressure value, forexample, in the first set of units may have the same value after theconversion as before the conversion. The CMP system 200 thus enable thequantization process to be performed with data from the relativelyaverage resolution digital devices (e.g. the controller 228), and rendersuch relatively average computational resolution of less importance inobtaining computed results having an acceptable accuracy, such as aboutone percent (1%), whereby quantization errors are eliminated orsignificantly reduced.

[0087] Although the foregoing invention has been described in somedetail for purposes of clarity of understanding, it will be apparentthat certain changes and modifications may be practiced within the scopeof the appended claims. Accordingly, the present embodiments are to beconsidered as illustrative and not restrictive, and the invention is notto be limited to the details given herein, but may be modified withinthe scope and equivalents of the appended claims.

What is claimed is:
 1. Apparatus for reducing quantization error in ananalog computation for converting an input representing force to ananalog force output representing force in terms of a force actuatorsignal to be input to a force actuator, wherein the input representingforce is based on an input resolution, the apparatus comprising: aprocessor programmed to convert the input to two analog force signalsand a plurality of digital logic signals, the analog force signalsrepresenting an analog upper end and an analog lower end of a range ofthe force actuator signal, the range including the value of the forceactuator signal, the digital logic signals having a resolution less thanor equal to 12 bits and being equal to the input resolution, the digitallogic signals representing the force actuator signal in the range; adifference circuit for generating an analog range voltage signalrepresenting the range of the force actuator signal; a divider circuitfor dividing the analog range voltage signal by the resolution of thedigital logic signals to output an analog force increment signal interms of voltage; first analog circuitry responsive to logic defined bythe digital logic signals for converting the analog force incrementsignal to an analog force set point signal; and second analog circuitryfor adding one of the analog force signals to the analog force set pointsignal to determine the value of the force actuator signal.
 2. Apparatusas recited in claim 1, wherein the first analog circuitry comprises:digital logic circuitry responsive to logic of the digital logic signalsfor selecting an analog logical voltage signal; and analog multipliercircuitry for multiplying the analog force increment signal by theanalog logical voltage signal to output a voltage value of the analogforce set point signal.
 3. Apparatus as recited in claim 1, wherein thefirst analog circuitry comprises: logic evaluation circuitry having onelogic input corresponding to each bit of the resolution of the digitallogic signals, the logic evaluation circuitry having one binary logicaloutput corresponding to each count of the resolution of the digitallogic signals; logic multiplier circuitry comprising one multipliercorresponding to each count of the resolution of the digital logicsignals, each multiplier having one binary logical input correspondingto each binary logical output, the multipliers having one logic voltageinput having different values selected according to the number of countsof the resolution of the digital logic signals, each multiplier having aset point factor output; a series of adder circuits for respectivelysequentially adding two of the set point factor outputs to produce afirst sum, the adder circuits adding a next set point factor to thefirst sum to produce a next sum and adding in sequence until a finalnext sum is a sum having a number one less that the value of the countof the resolution; and a multiplier circuit having the final next sum asa first input and the analog force increment signal as a second input,the multiplier outputting the analog force set point signal. 4.Apparatus for reducing quantization error in an analog computation forconverting an input representing force in terms of units of force to ananalog force output representing force in terms of a signal to be inputto a force actuator, the apparatus comprising: a processor programmed toconvert the input to two analog force signals and a plurality of digitallogic signals, the analog force signals representing the boundaries of arange of signals to be input to a force actuator, the range including aforce actuator signal having a value corresponding to the value of theforce in force units, each of the digital logic signals having aresolution less than or equal to 12 bits, the digital logic signalstogether representing the force actuator signals in the range having thevalue corresponding to the value of the force in force units; firstanalog circuitry responsive to the resolution of the digital logicsignals for converting a difference between the two analog force signalsto an analog force increment signal; second analog circuitry responsiveto logic defined by the digital logic signals for converting the analogforce increment signal to an analog force set point signal; and thirdanalog circuitry for adding one of the analog force signals to theanalog force set point signal to determine the value of the forceactuator signal.
 5. Apparatus as recited in claim 4, wherein the inputrepresenting force in terms of units of force is based on an inputresolution, and wherein the input resolution equals the resolution ofthe digital logic signals.
 6. Apparatus as recited in claim 4, whereinthe first analog circuitry comprises a difference circuit for generatingan analog range voltage signal representing the range of the forceactuator signal, the range being the difference between the two analogforce signals; and a divider circuit for dividing the analog rangevoltage signal by a function of the resolution of the digital signals tooutput the analog force increment signal in terms of voltage. 7.Apparatus as recited in claim 4, wherein the second analog circuitrycomprises: digital logic circuitry responsive to logic of the digitallogic signals for selecting an analog logical voltage signal; and analogmultiplier circuitry for multiplying the analog voltage force incrementsignal by the analog logical voltage signal to output a voltage value ofthe analog force set point signal.
 8. Apparatus as recited in claim 4,wherein the second analog circuitry comprises: logic evaluationcircuitry having one logic input corresponding to each bit of theresolution of the digital logic signals, the logic evaluation circuitryhaving one binary logical output corresponding to each count of theresolution of the digital logic signals; logic multiplier circuitrycomprising one multiplier corresponding to each count of the resolutionof the digital logic signals, each multiplier having one binary logicalinput corresponding to each binary logical output, the multipliershaving one logic voltage input having different values selectedaccording to the number of counts of the resolution of the digital logicsignals, each multiplier having a set point factor output; a series ofadder circuits for respectively sequentially adding two of the set pointfactor outputs to produce a first sum, the adder circuits adding a nextset point factor to the first sum to produce a next sum and adding insequence until a final next sum is a sum having a number one less thatthe value of the count of the resolution; and a multiplier circuithaving the final next sum as a first input and the analog forceincrement signal as a second input, the multiplier outputting the analogforce set point signal.
 9. Apparatus for reducing quantization error inan analog computation for converting an input representing force interms of units of force to an analog force output representing force interms of a force actuator signal to be input to a force actuator,wherein the input representing force in terms of units of force is basedon an input resolution; the apparatus comprising: a processor programmedto convert the input to two analog force signals and a plurality ofdigital logic signals, the analog force signals representing theboundaries of a range of force actuator signals to be input to a forceactuator, the range of the force actuator signals including the value ofa force actuator signal having a value corresponding to the value of theforce in force units; the digital logic signals having a resolutionequal to the input resolution and less than or equal to 12 bits, thedigital logic signals representing the force actuator signals in therange having the value corresponding to the value of the force in unitsof force; a difference circuit for generating an analog range voltagesignal representing the range of the force actuator signals, the rangebeing the difference between the two analog force signals; a dividercircuit for dividing the analog range voltage signal by the resolutionof the digital logic signals to output an analog force increment signalin terms of voltage; first analog circuitry responsive to logic definedby the digital logic signals for converting the analog force incrementsignal to an analog force set point signal; and second analog circuitryfor adding one of the analog force signals to the analog force set pointsignal to determine the value of the force actuator signal. 10.Apparatus as recited in claim 9, wherein the first analog circuitrycomprises: digital logic circuitry responsive to logic of the digitallogic signals for selecting an analog logical voltage signal; and analogmultiplier circuitry for multiplying the analog force increment signalby the analog logical voltage signal to output a voltage value of theanalog force set point signal.
 11. Apparatus as recited in claim 9,wherein the first analog circuitry comprises: logic evaluation circuitryhaving one logic input corresponding to each bit of the resolution ofthe digital logic signals, the logic evaluation circuitry having onebinary logical output corresponding to each count of the resolution ofthe digital logic signals; logic multiplier circuitry comprising onemultiplier corresponding to each count of the resolution of the digitallogic signals, each multiplier having one binary logical inputcorresponding to each binary logical output, the multipliers having onelogic voltage input having different values selected according to thenumber of counts of the resolution of the digital logic signals, eachmultiplier having a set point factor output; a series of adder circuitsfor respectively sequentially adding two of the set point factor outputsto produce a first sum, the adder circuits adding a next set pointfactor to the first sum to produce a next sum and adding in sequenceuntil a final next sum is a sum having a number one less that the valueof the count of the resolution; and a multiplier circuit having thefinal next sum as a first input and the analog force increment signal asa second input, the multiplier outputting the analog force set pointsignal.